WASHINGTON — President Obama leaves for Europe on Monday night cautiously optimistic that the crisis in Ukraine has turned a corner, but he will find himself face to face with President Vladimir V. Putin of Russia for the first time since the two squared off in a Cold-War-style showdown in Eastern Europe.

Mr. Obama’s trip to Poland, Belgium and France comes just days after Ukraine elected a pro-European president and Mr. Putin pulled Russian troops back from the border. American and European officials hope the developments have begun to defuse the crisis, and say they have decided to hold off any new sanctions on Russia absent fresh provocative action by Moscow.

But the situation in eastern Ukraine remains volatile, and specialists warn that Russia has not abandoned efforts to assert influence there. While American and European leaders breathe a sigh of relief, skeptics suggest Mr. Putin is playing for time, opting against an overt invasion that he may never have intended so as to lull the West while he cements his annexation of Crimea and works more quietly to disrupt eastern Ukraine without further penalty.

“So much of this is trying to read the mind of one guy who lives in Moscow, and that’s difficult,” said Richard Fontaine, president of the Center for a New American Security, a research organization. “What we may be facing is a fairly lengthy period where this low-grade stuff that the Russians can help foment together with these groups on the ground doing their thing — this is the reality for a fairly long period of time, which also serves Putin’s basic interest.”

In his speech at West Point last week, Mr. Obama cited Ukraine as a successful example of uniting the international community against a mutual threat. Susan E. Rice, his national security adviser, sounded a similar theme on Sunday.

“The United States, working with our European partners, has rallied to isolate and pressure Russia for its activities in Ukraine,” she said on “This Week,” an ABC News program. “That’s the kind of leadership that only the world’s greatest power can bring to bear.”

Ms. Rice was trying to rebut critics who maintain Mr. Obama has not been tough enough with Russia. “When America’s weak, when the American president is weak, it leaves our friends and allies vulnerable and it makes the world a lot more dangerous place,” Senator Ted Cruz, a Texas Republican who just returned from Ukraine, said on the same program.

White House officials said the president would use the trip to meet with the new Ukrainian leader, Petro O. Poroshenko, and to reassure Central and Eastern European allies of American support against Russian aggression. He will consult with allies about next steps, including weaning Europe off Russian gas. But aides said Mr. Obama was not declaring victory in Ukraine.

“We believe that the situation continues to be a crisis,” said Benjamin J. Rhodes, a deputy national security adviser. “There are people dying on a regular basis in eastern and southern Ukraine, given the violence perpetrated and initiated by separatist factions there. So by no means are we out of the woods on Ukraine.”

Mr. Obama arrives in Warsaw on Tuesday to meet not only with Polish leaders but also with leaders from throughout the region who will converge there. On Wednesday, he will meet with Mr. Poroshenko for the first time since his election and then address a public rally celebrating the 25th anniversary of the elections in Poland that signaled the eventual end of Communist rule.Later that day Mr. Obama will fly to Brussels, where he will meet that night and Thursday with counterparts from Britain, France, Germany, Italy, Canada and Japan in a reconstituted Group of 7. Their annual summit meeting was originally supposed to be hosted by Mr. Putin in Sochi, but Russia was suspended from the Group of 8 after the intervention in Ukraine.

If Mr. Putin is unwelcome in Brussels, however, he will be at Mr. Obama’s next stop in Paris. President François Hollande of France plans to host Mr. Obama for dinner on Thursday and host Mr. Putin separately that same evening. Mr. Obama and Mr. Putin will both be at Normandy on Friday for the 70th anniversary of the D-Day landings. No meetings are scheduled, but aides did not rule out an unscripted conversation.

Mr. Obama and the Europeans have struggled to stay together on sanctions, with the allies reluctant to jeopardize deeper economic ties with Russia and weary of confrontations beyond their borders. A survey by the Körber Foundation found that only 37 percent of Germans favor more involvement in international crises, compared with 62 percent in a comparable survey 20 years ago.

Chancellor Angela Merkel of Germany is crucial to the coalition facing Russia. In an interview with the Frankfurter Allgemeine Zeitung published on Friday, Frank-Walter Steinmeier, the foreign minister, called the Ukrainian election “a chance, but not a political solution to the conflict.”

British and French diplomats give Mr. Obama high marks for handling the Ukraine crisis, although they said he came late to understanding the potential Russian threat. In Paris, officials anticipate tension between Mr. Obama and Mr. Hollande over French plans to sell Mistral-class helicopter carriers to Russia.

Leaders in Poland and the Baltic republics hope Mr. Obama promises additional forces beyond the relatively small deployments sent there in recent weeks. Polish leaders said they hoped Mr. Obama would lay out a clear, unambiguous road map for dealing with a resurgent Russia.

“What we most need to hear from President Obama is what to do with Ukraine, how to deal with this new Russia,” said Aleksander Kwasniewski, the former president of Poland. “We are not interested in a confrontation with the Russians. We are not interested in Cold War II. But we will have a difficult time getting through the next four or five months without very clear and very determined American leadership.”

Poland has spent the last decade shifting focus from Washington to Berlin and Brussels, while nursing a raft of grievances and disappointments over what it saw as America’s inattention and insensitivity. Warsaw bristled when Mr. Obama canceled his predecessor’s plans to station interceptors in Poland as part of a missile defense system. But a reformulated missile defense program approved by Mr. Obama will include a site in Poland.

Bohdan Szklarski, president of the American Studies Center at the University of Warsaw, said that the trip was “an opportunity for Obama” but that he should avoid empty words. “When he is going over his speech, President Obama should cross out the platitudes we always hear, unless they are accompanied by something concrete,” he said.

Polish leaders said Mr. Obama’s trip vindicated their longstanding warnings about Russia. “The usual interpretation of the Polish position in the past has been, oh, it is these crazy Poles expressing their usual disdain for Russia,” said Aleksander Smolar, president of the Stefan Batory Foundation, which advocates civic engagement. “Now, however, people are taking the Polish position more seriously.”

A version of this article appears in print on , Section A, Page 5 of the New York edition with the headline: With Ukraine Crisis Cooling, Obama Sets Off to Soothe European Friends. Order Reprints | Today’s Paper | Subscribe